It is given that x2 - 6x + 14 = (x+p) +9 Find the value of p and q.
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<h2>Slope-intercept form</h2>
Linear equations are often organized in slope-intercept form:
- <em>(x,y)</em> = a point that falls on the line
- <em>m</em> = the slope of the line
- <em>b</em> = the y-intercept of the line
The slope of a line is equal to its .
- <em>"Rise"</em> refers to the number of units the line travels up.
- <em>"Run"</em> refers to the number of units the line travels to the right.
Typically, we would solve for the slope by using the following formula:
where two points that fall on the line are
and
The y-intercept of a line refers to the y-value that occurs when x=0.
On a graph, it is the y-value where the line crosses the y-axis.
<h2>Writing the Equation</h2>1) Determine the slope of the line (m)
Plug in the two given points, (-17,-4) and (-7,-13):
Therefore, the slope of the line is . Plug this into
:
2) Determining the y-intercept (b)
Plug in one of the given points and solve for b:
Therefore, the y-intercept of the line is . Plug this back into our equation: